K. G. Whitney

Basic considerations for scaling Z-pinch x-ray emission with atomic number

Two energies are identified that define the x‐ray emission characteristics of Z‐pinch array implosions. One, the kinetic energy per ion, is intensive, and the other, the kinetic energy per centimeter, is extensive. From a series of one‐dimensional axisymmetric hydrodynamic calculations, we have calculated the dependence of the x‐ray emission from aluminum implosions above 1 keV on these energies. These calculations are carried out for a specially chosen theoretical case where the kinetic energy that is generated during implosion is converted to thermal energy and x rays during the plasma collision on axis in the absence of current. In this case, we determine the I4 to I2 transition of the scaling of emission with peak current, I, as a parametric function of the kinetic energy per ion. We also determine a functional dependence of the emission on this energy when the mass of the imploded aluminum array is held fixed. It is seen that the ability of the plasma to radiate large amounts of energy in either I4 o...

K-shell line ratios and powers for diagnosing cylindrical plasmas of neon, aluminum, argon, and titanium

Abstract Detailed collisional-radiative-equilibrium calculations of the ratios of the first two resonance lines of the hydrogen- and helium-like ionic stages are presented as isocontours in temperature and density space along with the total power emitted from those stages. Taken together, the contours provide a one-to-one correspondence between line ratios and power outputs and the electron temperatures and ion densities of uniform, cylindrically symmetric, optically thick plasmas. The results are given for different sized neon, aluminum, argon, and titanium plasmas, and for temperatures which favor ionization to the K shell. The underlying physics determining the dependencies of the various quantities and some of the limitations of their application are discussed. These results are intended for use in the diagnosis of Z -pinch plasmas, and can provide insight into how their properties depend on generator and load design.

Titanium K-shell x-ray production from high velocity wire array implosions on the 20-MA Z accelerator

The advent of the 20-MA Z accelerator [R.B. Spielman, C. Deeney, G.A. Chandler, et al., Phys. Plasmas 5, 2105, (1997)] has enabled implosions of large diameter, high-wire-number arrays of titanium to begin testing Z-pinch K-shell scaling theories. The 2-cm long titanium arrays, which were mounted on a 40-mm diameter, produced between 75{+-}15 to 125{+-}20 kJ of K-shell x-rays. Mass scans indicate that, as predicted, higher velocity implosions in the series produced higher x-ray yields. Spectroscopic analyses indicate that these high velocity implosions achieved peak electron temperatures from 2.7{+-}0.1 to 3.2{+-}0.2 keV and obtained a K-shell emission mass participation of up to 12%.

Phenomenological modeling of turbulence in Z-pinch implosions

A phenomenological investigation into the effects of magnetohydrodynamic (MHD) turbulence on the initial stagnation dynamics of aluminum wire array and argon gas puff Z‐pinch implosions is performed. The increases that turbulence produces in the plasma viscosity, heat conductivity, and electrical resistivity are modeled by using multipliers for these quantities in one‐dimensional (1‐D) MHD calculations. The major effect of these increases is to soften the 1‐D implosions by decreasing the densities that are achieved on axis at stagnation. As a consequence, a set of multipliers can be found that reasonably duplicates the average electron temperatures, ion densities, and mass of the K‐shell emission region that were measured at stagnation for a variety of Physics International aluminum wire array and argon gas puff experiments. It is determined that the dependence of these measured quantities on the multipliers is weak once a level of enhancement is reached, where agreement between calculations and experimen...

Direct solution of the equation of transfer using frequency- and angle-averaged photon escape probabilities, with application to a multistage, multilevel aluminum plasma

Abstract : A formalism is developed which permits direct steady-state solution of the transfer equation using escape probabilities probabilities averaged over angle and frequency. A matrix of probability-based coupling coefficients, which are related to the kernel K1 is used to obtain the source function for a doppler profile in plane-parallel geometry. Comparison is made with exact solutions, establishing the high accuracy of the technique. The method is extendable to different physical situations by simply modifying the coupling coefficients. (Author)

Dynamics of a high-power aluminum-wire array Z-pinch implosion

Annular Al-wire Z-pinch implosions on the Saturn accelerator [D. D. Bloomquist et al., Proceedings, 6th Pulsed Power Conference (Institute of Electrical and Electronics Engineers, New York, 1987), p. 310] that have high azimuthal symmetry exhibit both a strong first and weaker second x-ray burst that correlate with strong and weaker radial compressions, respectively. Measurements suggest that the observed magnetic Rayleigh–Taylor (RT) instability prior to the first compression seeds an m=0 instability observed later. Analyses of axially averaged spectral data imply that, during the first compression, the plasma is composed of a hot core surrounded by a cooler plasma halo. Two-dimensional (2-D) radiation magnetohydrodynamic computer simulations show that a RT instability grows to the classic bubble and spike structure during the course of the implosion. The main radiation pulse begins when the bubble reaches the axis and ends when the spike finishes stagnating on axis and the first compression ends. These ...

Neon gas puff implosions on a high‐current microsecond generator with and without a plasma opening switch

Implosions of 2.5‐cm‐diam neon gas shells on a 1.2 μs quarter‐period, 3 MA driver, FALCON, have produced no more than 7.6 kJ of kilovolt neon K‐shell radiation. The incorporation of a plasma opening switch produces faster current pulses: up to 1.8 MA in 190 ns. With the higher rate of rise of current, neon gas puffs have produced up to 13.5 kJ of kilovolt K‐shell radiation. Numerical calculations indicate that this increase in radiation is due to the achievement of a higher kinetic energy per ion at higher current levels. Spectroscopic measurements confirm that a significant fraction of the plasma is heated into the K‐shell ionization states and that the faster current pulses increase this fraction up to 40%.

Plasma conditions required for attainment of maximum gain in resonantly photo-pumped aluminum XII and neon IX

We present a detailed analysis of the plasma conditions required to optimize gain in two proposed x‐ray lasing schemes using resonant photo‐pumping. In one proposed configuration, the Si XIII line 1s2‐1s2p1P at 6.650 A pumps Al XII 1s2−1s3p1P at 6.635 A, inverting the Al XII n = 3 and n = 2 levels which are separated by 44 A. A similar approach which utilizes the Na X 1s2‐1s2p1P line at 11.00 A would invert the n = 4, 3, and 2 levels of Ne IX. Conditions in the pumped neon and aluminum plasmas, and in the pumping silicon plasma, are calculated using a multistage, multilevel atomic model with multifrequency radiation transport. For modeling the pumping sodium line we have inferred the intensity from a spectrum of a neon filled, laser‐imploded glass microballoon containing sodium impurities obtained at Rochester. The pump line intensities calculated for Si and inferred for Na are equivalent to blackbodies of 252 and 227 eV, respectively. It is found that peak gain for the 3‐2 lines of about 100 cm−1 occurs ...

Transition from I4 to I2 scaling of K-shell emission in aluminum array implosions

Abstract It has been observed experimentally that optimal K-shell emission scales as I4 over a limited range of currents in Z-pinch imploded plasmas. It is also known that in order to conserve energy at a sufficiently high current level, this scaling must change and become less than or equal to I2. This result follows because the energy sources, PdV work and ohmic heating scale as I2. In this work, we study theoretically how the scaling of K-shell emission changes as the current is progressively increased. This study is based on a comparison of the implosion characteristics of a number of 1-D radiation hydrodynamic simulations of imploding aluminum wire arrays in which it is assumed that X-ray emission occurs primarily as a result of thermalization of kinetic energy and that the maximum kinetic-energy-per-ion that is generated before the plasma stagnates on axis is kept constant while the mass and current are increased. Results are presented that show the range of validity of previously developed phenomenological models that examined I4 scaling. In addition, the roles that opacity, initial conditions, total mass, density, temperature, and the strength of the magnetic field play in influencing the scaling of total, and K-shell emissions as the current is increased are discussed.

The physics of radiation transport in dense plasmas

Radiation transport redistributes energy within a medium through the emission and reabsorption of photons. These processes also have a pronounced effect on the spectrum of radiation that escapes the medium. As the deliverable energies of plasma drivers such as lasers and pulsed-power generators steadily increase, denser and/or more massive plasmas can be created. Such plasmas are more absorptive to their own emitted radiation, with portions of the line spectrum frequently being highly opaque. Thus, radiation transport becomes more important, along with the need to consider its impact on the design of experiments and their diagnosis. This tutorial paper covers the basic theory and equations describing radiation transport, its physical effects, experimental examples of transport phenomena, and current challenges and issues. Among the specific topics discussed are requirements for local thermodynamic equilibrium (LTE), conditions for diffusion and the use of the diffusion approximation, the formation of emis...